MinT - Best Known (120−74, 120, s)-Nets in Base 9

Best Known (120−74, 120, s)-Nets in Base 9

(120−74, 120, 81)-Net over F₉ — Constructive and digital

Digital (46, 120, 81)-net over F₉, using

t-expansion [i] based on digital (32, 120, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(120−74, 120, 162)-Net over F₉ — Digital

Digital (46, 120, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(120−74, 120, 2256)-Net in Base 9 — Upper bound on s

There is no (46, 120, 2257)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 281518 242295 734728 877241 958282 140209 231104 606381 156234 909922 092425 162847 117378 273510 624733 184896 161329 502210 811945 > 9¹²⁰ [i]